Nonlinear Skew Lie Triple Derivations between Factors

Abstract Let A be a factor. For A, B ∈4, define by [A, B]. = AB- BA＊ the skew Lie product of A and B. In this article, it is proved that a map φ： A- A satisfies φ（[[A, B]., C].） = [[φ（A）, B]., C]. ＋ [[A, φ（B）]. C]. ＋ [[A, B]., φ（C）]. for all A, B, C∈ A if and only if φ is an additive ＊-derivation....

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 32; no. 7; pp. 821 - 830
Main Authors Li, Chang Jing, Zhao, Fang Fang, Chen, Quan Yuan
Format Journal Article
LanguageEnglish
Published Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.07.2016
Springer Nature B.V
Subjects
Algebra
Derivation
Equality
Hilbert space
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Nonlinearity
Studies
Theorems
三倍数
传递因数
添加剂
非线性
47B49
derivation
factor
Skew Lie triple derivation
46L10
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Summary:Abstract Let A be a factor. For A, B ∈4, define by [A, B]. = AB- BA＊ the skew Lie product of A and B. In this article, it is proved that a map φ： A- A satisfies φ（[[A, B]., C].） = [[φ（A）, B]., C]. ＋ [[A, φ（B）]. C]. ＋ [[A, B]., φ（C）]. for all A, B, C∈ A if and only if φ is an additive ＊-derivation.
Bibliography:Skew Lie triple derivation, derivation, factor
11-2039/O1
Abstract Let A be a factor. For A, B ∈4, define by [A, B]. = AB- BA＊ the skew Lie product of A and B. In this article, it is proved that a map φ： A- A satisfies φ（[[A, B]., C].） = [[φ（A）, B]., C]. ＋ [[A, φ（B）]. C]. ＋ [[A, B]., φ（C）]. for all A, B, C∈ A if and only if φ is an additive ＊-derivation.
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-016-5690-1